Optimal reinsurance–investment policies for insurers with mispricing under mean-variance criterion

Abstract

This article studies the optimal mean-variance reinsurance-investment selection for insurers with mispricing. Assuming that insurers wish to purchase proportional/excess-of-loss reinsurance and exchange among a risk-free asset, a pair of mispriced stocks, and the market index to maximize their return and minimize the risk. Using the approach developed by Björk, Khapko, and Murgoci (Finance and Stochastics 2017; 21 (2):331–60), we derive the equilibrium strategies and the corresponding equilibrium value functions under two cases through solving the extended Hamilton–Jacobi–Bellman system. Moreover, numerical analyses are provided to illustrate our results.

Keywords:

• Reinsurance–investment
• mispricing
• mean-variance
• equilibrium strategies
• extended HJB system

Additional information

Funding

This work is supported by the grants from the National Natural Science Foundation of China (Nos. 71701068, 11701175, 11671132), the Natural Science Foundation of Hunan Province, China (No. 2018JJ3360), and the Scientific Research Fund of Hunan Provincial Education Department, China (Nos. 19B343, 19A342), and the Applied Economics of Hunan Province.